1. Intro to Similarity Unit#5

2. Power Word definitions
Ratio- a comparison between 2
Proportion – a statement in which two ratios are equal
Scale Factor – The ratio of any two corresponding lengths in two similar geometric figures.
Similar figures – figures whose corresponding sides have lengths that are proportional and whose corresponding angles are congruent.

3. Theorem: In a proportion, the product of the means equals the product of the extremes.
2 ways to write a proportion:
1) )
Write a proportion using: 25, 45, 5, Solve for b. b+ 5 : 7 = 5 :10
𝑏+5 7 = 5 10
25:5=45:9
10(b+ 5) = 7(5)
10b+50=35
10b = -15
b= -1.5
225=225

4. Solve for x.

5. What makes 2 shapes similar?
Corresponding angles are congruent!
Corresponding sides
are in proportion!
4:2 = 2:1

6. 𝐴𝐵 𝑋𝑌 𝐴𝐶 𝑋𝑍 𝐵𝐶 𝑌𝑍

7. What is the scale factor or ratio of similitude of the quadrilaterals?
8 4 = 4 2 = 6 3
So ratio of similitude is 2:1!
2 1 = 5 𝑁𝑀
2(NM)=5
NM=2.5

8. What evidence suggests the 2 triangles are similar?
Parallel lines cut by a transversal form alternate interior angles that are congruent.
Right angles are formed and congruent.
If 2 corresponding pairs of angles in a triangle are congruent, then the 3rd pair is as well!

9. x
150
450
Label the diagram
100
𝑥 450 =
100x=67,500
X=675 cm

10. Scale drawings/maps Legs: 4:6, so 2:3 but bases are 1:1
Finding actual distance Examples:
Maps: What is the actual distance
between Hagerstown and Annapolis?
Identify the scale factor 2)
Legs: 4:6, so 2:3
but bases are 1:1
All sides must be in the same scale factor, so these are not similar trapezoids!
About 4, so 4(24) =96 miles

11. Alex wants to reduce a figure that is 9 inches tall and 16 inches wide so that it will fit on a 9-inch-by-12-inch piece of paper. If he reduces the figure proportionally, what is the maximum size the reduced figure could measure?
15(4.5)=67.5 mm
30(4.5) = mm 16 9 12
16 12 = 9 𝑥
So, 16x =108 x=6.75

12. 𝑥+2 6 = 15 𝑥+1 x=-11 and x=8 10 6 = 20 𝐷𝐹 DF=12 (x+2)(x+1)=90
Algebraically
speaking… 10
𝑥+2 6 = 15 𝑥+1
(x+2)(x+1)=90
(x+11)(x-8)=0
𝑥 2 +3x+2=90
𝑥 2 +3x-88=0
x=-11 and x=8
Factor!
Substitute 8…
10 6 = 20 𝐷𝐹
DF=12

13. 78𝑚 90𝑚 = 𝑥𝑐𝑚 36𝑐𝑚 𝑥=31.2 cm 4(4x+3) =60 16x+12=60 16x=48 X=3
1) Solve for x.
4(4x+3) =60
16x+12=60
16x=48
X=3 2)
78𝑚 90𝑚 = 𝑥𝑐𝑚 36𝑐𝑚
𝑥=31.2 cm

14. 3) A Barbie doll is made to have a ratio of similitude of roughly 1:6 with a real 5’6” human being. If a Barbie doll has a waist size of 2.5 inches, how would you compute her “real-life” waist size?
Hmm…Barbie is not very well modeled after a real person!
1 6 = 2.5 𝑥
𝑥=15 𝑖𝑛𝑐ℎ𝑒𝑠